[Haskell-beginners] Re: [Haskell-cafe] represent data sturcture using function

Bonus points if you find the stupid bug in my code :) -- ryan On Mon, Dec 29, 2008 at 1:48 AM, Ryan Ingram wrote:

On Sun, Dec 28, 2008 at 10:13 PM, David Menendez wrote:

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2008/12/29 Raeck chiu :

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It seems to be very difficult to change the number of Male or Female if a concrete data structure is not used. Is it possible change the number of Male in classA when represent classA using function?

Here's the simplest way:

update k v map = \k' -> if k' == k then v else map k'

Note that it requires an Eq instance for Sex.

let classA' = update Male 150 classA in (classA' Male, classA' Female) = (150,200)

Of course this version of update leaks crazy amounts of memory:

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let bigmap = iterate (update Male 150) classA !! 100000 bigmap Male

"bigmap" leaves a huge chain of thunks pointing at each other, which can never be freed.

Using functions is mathematically more elegant than some concrete data structure (which might require Eq or Ord or other constraints, and have multiple observable representations for the same map, or have maps that don't include every element).

However, "generic maps" have been improving a lot recently, especially with data families in the new GHC. You use an abstract type (k :-> v) to represent the map; this type is semantically equivalent to (k -> v) via some observation function for generic maps, but has a compact representation. For example:

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class MapKey k where data k :-> v newMap :: (k -> v) -> (k :-> v) fetch :: (k :-> v) -> (k -> v) update :: (k,v) -> (k :-> v) -> (k :-> v) empty :: v -> (k :-> v) empty = newMap (const v)

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instance MapKey Bool where data Bool :-> v = BoolMap v v newMap f = BoolMap (f False) (f True) fetch (Boolmap t f) v = if v then t else f update (True, t) (BoolMap _ f) = Boolmap t f update (False, f) (BoolMap t _) = Boolmap t f

"fetch" converts this representation of a total function over k, into an actual function. The representation of k :-> v might vary depending on k; Int might use IntMap, (k1,k2) can compose maps:

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instance (MapKey k1, MapKey k2) => MapKey (k1,k2) where newtype (k1,k2) :-> v = PairMap (k1 :-> (k2 :-> v)) ...

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instance (MapKey k1, MapKey k2) => MapKey (Either k1 k2) where data (Either k1 k2) :-> v = EitherMap (k1 :-> v) (k2 :-> v) ...

This gives you the same benefits as the function approach but without the terrible performance issues. You do need to write instances for your types, though, although most can be easily derived from the instances for pairs, Either, and Integer.

See http://www.haskell.org/haskellwiki/GHC/Indexed_types for more.

-- ryan